In underwater sonar systems, identifying targets from their signatures is an important, but, yet, open problem. The Matrix Pencil approach allows us to extract the modes (and mode amplitudes) of a decaying time domain signal. The main premise of this effort was that the modes are uniquely associated with individual targets and, hence, obtaining the modes should help target identification. This report presents the results of the use of the Matrix Pencil approach applied to the PondEX data sets provided by Defense Research and Development Canada (DRDC) Atlantic. The data set includes the sonar returns from a variety of targets and target-like objects from many along-track aspect angles and target orientations. As our results will show, in our analysis the Matrix Pencil approach is able to distinguish between two very different kinds of targets. We also discuss more cautionary results using comparisons of similar objects in different settings. However, we conclude that there is some promise in the notion of target discrimination and identification using the Matrix Pencil approach.